arXiv subjects

H. Lu

Publications and source records attributed to H. Lu.

At least 343 records · Page 19Linked to original sources

arXiv2002

SU(2) Reduction of Six-dimensional (1,0) Supergravity

We obtain a gauged supergravity theory in three dimensions with eight real supersymmetries by means of a Scherk-Schwarz reduction of pure N=(1,0) supergravity in six dimension on the SU(2) group manifold. The SU(2) Yang-Mills fields in the model propagate, since they have an ordinary kinetic term in addition to Chern-Simons couplings. The other propagating degrees of freedom consist of a dilaton, five scalars which parameterise the coset SL(3,R)/SO(3), three vector fields in the adjoint of SU(2), and twelve spin 1/2 fermions. The model admits an AdS_3 vacuum solution. We also show how a charged black hole solution can be obtained, by performing a dimensional reduction of the rotating self-dual string of six-dimensional (1,0) supergravity.

hep-th↗

arXiv2002

The Radion Mode in Consistent Brane-World Reductions

We construct consistent brane-world Kaluza-Klein reductions involving the radion mode that measures the separation of the domain-wall branes. In these new examples, we can obtain matter supermultiplets coupled to supergravity on the brane, starting from pure gauged supergravity in the higher dimension. This contrasts with previously-known examples of consistent brane-world reductions involving the radion, where either pure supergravity reduced to pure supergravity, or else supergravity plus matter reduced to supergravity plus matter. As well as considering supersymmetric reductions, we also show that there exist broader classes of consistent reductions of bosonic systems. These include examples where the lower-dimensional theory has non-abelian Yang-Mills fields and yet the scalar sector has a potential that admits Minkowski spacetime as a solution. Combined with a sphere reduction to obtain the starting point for the brane-world reduction, this provides a Kaluza-Klein mechanism for obtaining non-abelian gauge symmetries from the geometry of the reduction, whilst still permitting a Minkowski vacuum in the lower dimension.

hep-th↗

arXiv2002

Linearly-realised Worldsheet Supersymmetry in pp-wave Background

We study the linearly-realised worldsheet supersymmetries in the ``massive'' type II light-cone actions for pp-wave backgrounds. The pp-waves have have 16+N_sup Killing spinors, comprising 16 ``standard'' Killing spinors that occur in any wave background, plus N_sup ``supernumerary'' Killing spinors (0\le N_sup \le 16) that occur only for special backgrounds. We show that only the supernumerary Killing spinors give rise to linearly-realised worldsheet supersymmetries after light-cone gauge fixing, while the 16 standard Killing spinors describe only non-linearly realised inhomogeneous symmetries. We also study the type II actions in the physical gauge, and we show that although in this case the actions are not free, there are now linearly-realised supersymmetries coming both from the standard and the supernumerary Killing spinors. In the physical gauge, there are no mass terms for any worldsheet degrees of freedom, so the masses appearing in the light-cone gauge may be viewed as gauge artefacts. We obtain type IIA and IIB supergravity solutions describing solitonic strings in pp-wave backgrounds, and show how these are related to the physical-gauge fundamental string actions. We study the supersymmetries of these solutions, and find examples with various numbers of Killing spinors, including total numbers that are odd.

hep-th↗

arXiv2002

M-theory PP-waves, Penrose Limits and Supernumerary Supersymmetries

We study supersymmetric pp-waves in M-theory, their dimensional reduction to D0-branes or pp-waves in type IIA, and their T-dualisation to solutions in the type IIB theory. The general class of pp-waves that we consider encompass the Penrose limits of AdS_p\times S^q with (p,q)=(4,7), (7,4), (3,3), (3,2), (2,3), (2,2), but includes also many other examples that can again lead to exactly-solvable massive strings, but which do not arise from Penrose limits. All the pp-waves in D=11 have 16 ``standard'' Killing spinors, but in certain cases one finds additional, or ``supernumerary,'' Killing spinors too. These give rise to linearly-realised supersymmetries in the string or matrix models. A focus of our investigation is on the circumstances when the Killing spinors are independent of particular coordinates (x^+ or transverse-space coordinates), since these will survive at the field-theory level in dimensional reduction or T-dualisation.

hep-th↗

arXiv2002

T-Duality in the Green-Schwarz Formalism, and the Massless/Massive IIA Duality Map

We derive a component-field expansion of the Green-Schwarz action for the type IIA string, in an arbitrary background of massless NS-NS and R-R bosonic fields, up to quadratic order in the fermionic coordinates θ. Using this action, we extend the usual derivation of Buscher T-duality rules to include not only NS-NS, but also R-R fields. Our implementation of the T-duality transformation rules makes use of adapted background-field parametrizations, which provide a more geometrically natural and elegant description for the duality maps than the ones previously presented. These T-duality rules allow us to derive the Green-Schwarz action for the type IIB string in an arbitrary background of massless NS-NS and R-R bosonic fields, up to O(θ^2). Implemention of another T-duality transformation on this type IIB action then allows us also to derive the Green-Schwarz action for the massive IIA string. By further considering T-duality transformations for backgrounds with the two U(1) isometries of a 2-torus, we give a string-theoretic derivation of the direct T-duality relation between the massless and massive type IIA strings. In addition, we give an explicit construction of the D=8 SL(3,R)xSL(2,R) invariant supergravity with two mass parameters that form a doublet under the SL(2,R) factor.

hep-th↗

arXiv2002

Special Holonomy Spaces and M-theory

We review the construction of regular p-brane solutions of M-theory and string theory with less than maximal supersymmetry whose transverse spaces have metrics with special holonomy, and where additional fluxes allow for brane resolutions via transgression terms. We summarize properties of resolved M2-branes and fractional D2-branes, whose transverse spaces are Ricci flat eight-dimensional and seven-dimensional spaces of special holonomy. Recent developments in the construction of new G_2 holonomy spaces are also reviewed.

hep-th↗

arXiv2002

Bianchi IX Self-dual Einstein Metrics and Singular G_2 Manifolds

We construct explicit cohomogeneity two metrics of G_2 holonomy, which are foliated by twistor spaces. The twistor spaces are S^2 bundles over four-dimensional Bianchi IX Einstein metrics with self-dual (or anti-self-dual) Weyl tensor. Generically the 4-metric is of triaxial Bianchi IX type, with SU(2) isometry. We derive the first-order differential equations for the metric coefficients, and obtain the corresponding superpotential governing the equations of motion, in the general triaxial Bianchi IX case. In general our metrics have singularities, which are of orbifold or cosmic-string type. For the special case of biaxial Bianchi IX metrics, we give a complete analysis their local and global properties, and the singularities. In the triaxial case we find that a system of equations written down by Tod and Hitchin satisfies our first-order equations. The converse is not always true. A discussion is given of the possible implications of the singularity structure of these spaces for M-theory dynamics.

hep-th↗

arXiv2002

New G_2 metric, D6-branes and Lattice Universe

We construct a new (singular) cohomogeneity-three metric of G_2 holonomy. The solution can be viewed as a triple intersection of smeared Taub-NUTs. The metric comprises three non-compact radial-type coordinates, with the principal orbits being a T^3 bundle over S^1. We consider an M-theory vacuum (Minkowski)_4\times M_7 where M_7 is the G_2 manifold. Upon reduction on a circle in the T^3, we obtain the intersection of a D6-brane, a Taub-NUT and a 6-brane with R-R 2-form flux. Reducing the solution instead on the base space S^1, we obtain three intersecting 6-branes all carrying R-R 2-form flux. These two configurations can be viewed as a classical flop in the type IIA string theory. After reducing on the full principal orbits and the spatial world-volume, we obtain a four-dimensional metric describing a lattice universe, in which the three non-compact coordinates of the G_2 manifold are identified with the spatial coordinates of our universe.

hep-th↗

arXiv2002

Penrose Limits of Non-standard Brane Intersections

The non-standard intersection of two 5-branes and a string can give rise to AdS_3\times S^3\times S^3\times S^1. We consider the Penrose limit of this geometry and study the supersymmetry of the resulting pp-wave solution. There is a one-parameter family of Penrose limits associated with the orthogonal rotation of the two foliating circles within the two 3-spheres. Supernumerary Killing spinors arise only when the rotation angle is 45 degrees, for which case we obtain the corresponding light-cone string action that has linearly-realised supersymmetry. We also obtain Penrose limits of other non-standard intersections that give rise to the product of AdS_3 or AdS_2 and two spheres. The resulting pp-waves are supported by multiple constant field strengths.

hep-th↗

arXiv2002

General Metrics of G_2 Holonomy and Contraction Limits

We obtain first-order equations for G_2 holonomy of a wide class of metrics with S^3\times S^3 principal orbits and SU(2)\times SU(2) isometry, using a method recently introduced by Hitchin. The new construction extends previous results, and encompasses all previously-obtained first-order systems for such metrics. We also study various group contractions of the principal orbits, focusing on cases where one of the S^3 factors is subjected to an Abelian, Heisenberg or Euclidean-group contraction. In the Abelian contraction, we recover some recently-constructed G_2 metrics with S^3\times T^3 principal orbits. We obtain explicit solutions of these contracted equations in cases where there is an additional U(1) isometry. We also demonstrate that the only solutions of the full system with S^3\times T^3 principal orbits that are complete and non-singular are either flat R^4 times T^3, or else the direct product of Eguchi-Hanson and T^3, which is asymptotic to R^4/Z_2\times T^3. These examples are in accord with a general discussion of isometric fibrations by tori which, as we show, in general split off as direct products. We also give some (incomplete) examples of fibrations of G_2 manifolds by associative 3-tori with either T^4 or K3 as base.

hep-th↗

arXiv2002

Almost Special Holonomy in Type IIA&M Theory

We consider spaces M_7 and M_8 of G_2 holonomy and Spin(7) holonomy in seven and eight dimensions, with a U(1) isometry. For metrics where the length of the associated circle is everywhere finite and non-zero, one can perform a Kaluza-Klein reduction of supersymmetric M-theory solutions (Minkowksi)_4\times M_7 or (Minkowksi)_3\times M_8, to give supersymmetric solutions (Minkowksi)_4\times Y_6 or (Minkowksi)_3\times Y_7 in type IIA string theory with a non-singular dilaton. We study the associated six-dimensional and seven-dimensional spaces Y_6 and Y_7 perturbatively in the regime where the string coupling is weak but still non-zero, for which the metrics remain Ricci-flat but that they no longer have special holonomy, at the linearised level. In fact they have ``almost special holonomy,'' which for the case of Y_6 means almost Kahler, together with a further condition. For Y_7 we are led to introduce the notion of an ``almost G_2 manifold,'' for which the associative 3-form is closed but not co-closed. We obtain explicit classes of non-singular metrics of almost special holonomy, associated with the near Gromov-Hausdorff limits of families of complete non-singular G_2 and Spin(7) metrics.

hep-th↗

arXiv2002

S^1-wrapped D3-branes on Conifolds

We construct a D3-brane wrapped on S^1, which is fibred over the resolved conifold as its transverse space. Whereas a fractional D3-brane on the resolved conifold is not supersymmetric and has a naked singularity, our solution is supersymmetric and regular everywhere. We also consider an $S^1$-wrapped D3-brane on the resolved cone over T^{1,1}/Z_2, as well as on the deformed conifold. In the former case, we obtain a regular supergravity dual to a certain four-dimensional field theory whose Lorentz and conformal symmetries are broken in the IR region and restored in the UV limit.

hep-th↗

arXiv2002

Resolution of Overlapping Branes

We obtain singularity resolutions for various overlapping brane configurations, including those of two heterotic 5-branes, type II 5-branes or D4-branes. In these solutions, the ``harmonic'' function H for each brane component depends only on the associated four-dimensional relative transverse space. The resolution is achieved by replacing these transverse spaces with Eguchi-Hanson or Taub-NUT spaces, both of which admit a normalisable self-dual (or anti-self-dual) harmonic 2-form. Due to the manner in which the interaction terms for the form fields modify their Bianchi identities or equations of motion, these normalisable harmonic 2-forms provide regular sources for the branes. We also obtain resolved 5-branes and D4-branes wrapped on S^1, which is fibred over the transverse Eguchi-Hanson or Taub-NUT spaces. The T-duality invariance of the NS-NS 5-brane is retained after the resolution. The resolved 5-branes and D4-branes provide regular supergravity duals of certain supersymmetric Yang-Mills theories in five and four dimensions.

hep-th↗

arXiv2002

New Cohomogeneity One Metrics With Spin(7) Holonomy

We construct new explicit non-singular metrics that are complete on non-compact Riemannian 8-manifolds with holonomy Spin(7). One such metric, which we denote by A_8, is complete and non-singular on R^8. The other complete metrics are defined on manifolds with the topology of the bundle of chiral spinors over S^4, and are denoted by B_8^+, B_8^- and B_8. The metrics on B_8^+ and B_8^- occur in families with a non-trivial parameter. The metric on B_8 arises for a limiting value of this parameter, and locally this metric is the same as the one for A_8. The new Spin(7) metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP^3. We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L^2-normalisable harmonic 4-form for the A_8 manifold, and two such 4-forms (of opposite dualities) for the B_8 manifold.

math.DG↗

arXiv2001

A G_2 Unification of the Deformed and Resolved Conifolds

We find general first-order equations for G_2 metrics of cohomogeneity one with S^3\times S^3 principal orbits. These reduce in two special cases to previously-known systems of first-order equations that describe regular asymptotically locally conical (ALC) metrics \bB_7 and \bD_7, which have weak-coupling limits that are S^1 times the deformed conifold and the resolved conifold respectively. Our more general first-order equations provide a supersymmetric unification of the two Calabi-Yau manifolds, since the metrics \bB_7 and \bD_7 arise as solutions of the {\it same} system of first-order equations, with different values of certain integration constants. Additionally, we find a new class of ALC G_2 solutions to these first-order equations, which we denote by \wtd\bC_7, whose topology is an \R^2 bundle over T^{1,1}. There are two non-trivial parameters characterising the homogeneous squashing of the T^{1,1} bolt. Like the previous examples of the \bB_7 and \bD_7 ALC metrics, here too there is a U(1) isometry for which the circle has everywhere finite and non-zero length. The weak-coupling limit of the \wtd\bC_7 metrics gives S^1 times a family of Calabi-Yau metrics on a complex line bundle over S^2\times S^2, with an adjustable parameter characterising the relative sizes of the two S^2 factors.

hep-th↗

arXiv2001

M-theory Conifolds

Seven-manifolds of G_2 holonomy provide a bridge between M-theory and string theory, via Kaluza-Klein reduction to Calabi-Yau six-manifolds. We find first-order equations for a new family of G_2 metrics D_7, with S^3\times S^3 principal orbits. These are related at weak string coupling to the resolved conifold, paralleling earlier examples B_7 that are related to the deformed conifold, allowing a deeper study of topology change and mirror symmetry in M-theory. The D_7 metrics' non-trivial parameter characterises the squashing of an S^3 bolt, which limits to S^2 at weak coupling. In general the D_7 metrics are asymptotically locally conical, with a nowhere-singular circle action.

hep-th↗

arXiv2001

Orientifolds and Slumps in G_2 and Spin(7) Metrics

We discuss some new metrics of special holonomy, and their roles in string theory and M-theory. First we consider Spin(7) metrics denoted by C_8, which are complete on a complex line bundle over CP^3. The principal orbits are S^7, described as a triaxially squashed S^3 bundle over S^4. The behaviour in the S^3 directions is similar to that in the Atiyah-Hitchin metric, and we show how this leads to an M-theory interpretation with orientifold D6-branes wrapped over S^4. We then consider new G_2 metrics which we denote by C_7, which are complete on an R^2 bundle over T^{1,1}, with principal orbits that are S^3\times S^3. We study the C_7 metrics using numerical methods, and we find that they have the remarkable property of admitting a U(1) Killing vector whose length is nowhere zero or infinite. This allows one to make an everywhere non-singular reduction of an M-theory solution to give a solution of the type IIA theory. The solution has two non-trivial S^2 cycles, and both carry magnetic charge with respect to the R-R vector field. We also discuss some four-dimensional hyper-Kahler metrics described recently by Cherkis and Kapustin, following earlier work by Kronheimer. We show that in certain cases these metrics, whose explicit form is known only asymptotically, can be related to metrics characterised by solutions of the su(\infty) Toda equation, which can provide a way of studying their interior structure.

hep-th↗

arXiv2001

Cohomogeneity One Manifolds of Spin(7) and G(2) Holonomy

In this paper, we look for metrics of cohomogeneity one in D=8 and D=7 dimensions with Spin(7) and G_2 holonomy respectively. In D=8, we first consider the case of principal orbits that are S^7, viewed as an S^3 bundle over S^4 with triaxial squashing of the S^3 fibres. This gives a more general system of first-order equations for Spin(7) holonomy than has been solved previously. Using numerical methods, we establish the existence of new non-singular asymptotically locally conical (ALC) Spin(7) metrics on line bundles over \CP^3, with a non-trivial parameter that characterises the homogeneous squashing of CP^3. We then consider the case where the principal orbits are the Aloff-Wallach spaces N(k,\ell)=SU(3)/U(1), where the integers k and \ell characterise the embedding of U(1). We find new ALC and AC metrics of Spin(7) holonomy, as solutions of the first-order equations that we obtained previously in hep-th/0102185. These include certain explicit ALC metrics for all N(k,\ell), and numerical and perturbative results for ALC families with AC limits. We then study D=7 metrics of $G_2$ holonomy, and find new explicit examples, which, however, are singular, where the principal orbits are the flag manifold SU(3)/(U(1)\times U(1)). We also obtain numerical results for new non-singular metrics with principal orbits that are S^3\times S^3. Additional topics include a detailed and explicit discussion of the Einstein metrics on N(k,\ell), and an explicit parameterisation of SU(3).

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